Comparison of Robustness and Efficiency for SIMPLE and CLEAR Algorithms with 13 High-Resolution Convection Schemes in Compressible Flows

REFERENCES

• M. M. Rahman and T. Siikonen , An Artificial Compressibility Method for Incompressible Flows , Numer. Heat Transfer B , vol. 40 , pp. 391 – 409 , 2001 .
   Web of Science ®Google Scholar
• K. C. Karki and S. V. Patankar , Pressure Based Calculation Procedure for Viscous Flows at all Speeds in Arbitrary Configurations , AIAA J. , vol. 27 , pp. 1167 – 1174 , 1989 .
   Google Scholar
• J. Rincon and E. Robin , A High Resolution Pressure Based Method for Compressible Flows , Comput. Fluids , vol. 26 , pp. 217 – 231 , 1997 .
   Web of Science ®Google Scholar
• M. H. Hu , J. S. Wu , and Y. S. Chen , Development of a Parallelized 2D/2D-Axisymmetric Navier–Stokes Equation Solver for All-Speed Gas Flows , Comput. Fluids , vol. 45 , pp. 241 – 248 , 2011 .
   Web of Science ®Google Scholar
• C. M. Xisto , J. C. Páscoa , P. J. Oliveira , and D. A. Nicolini , A Hybrid Pressure–Density-Based Algorithm for the Euler Equations at All Mach Number Regimes , Int. J. Numer. Meth. Fluids , vol. 70 , pp. 961 – 976 , 2012 .
   Web of Science ®Google Scholar
• Y. Y. Tsui and T. C. Wu , A Pressure-Based Unstructured-Grid Algorithm Using High-Resolution Schemes for All-Speed Flows , Numer. Heat Transf. B , vol. 53 , pp. 75 – 96 , 2008 .
   Web of Science ®Google Scholar
• F. Moukalled and M. Darwish , Pressure-Based Algorithms for Multifluid Flow at All Speeds—Part I: Mass Conservation Formulation, Numer. Heat Transfer B , vol. 45, pp. 495–522, 2004.
   Web of Science ®Google Scholar
• F. Moukalled and M. Darwish , Pressure-Based Algorithms for Multifluid Flow at All Speeds—Part II: Geometric Conservation Formulation , Numer. Heat Transfer B , vol. 45 , pp. 523 – 540 , 2004 .
   Web of Science ®Google Scholar
• H. I. Choi , D. Lee , and J. S. Maeng , A Node-Centered Pressure-Based Method for All Speed Flows on Unstructured Grids , Numer. Heat Transfer B , vol. 44 , pp. 165 – 185 , 2003 .
   Web of Science ®Google Scholar
• S. V. Patankar and D. B. Spalding , A Calculation Procedure for Heat Mass and Momentum Transfer in Three Dimensional Parabolic Flows , Int. J. Heat Mass Transfer , vol. 15 , pp. 1787 – 1806 , 1972 .
   Web of Science ®Google Scholar
• K. C. Karki and S. V. Patankar , Pressure Based Calculation Procedure for Viscous Flows at All Speeds in Arbitrary Configurations , AIAA J. , vol. 27 , pp. 1167 – 1174 , 1989 .
   Google Scholar
• W. Q. Tao , Z. G. Qu , and Y. L. He , A Novel Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems—CLEAR (Coupled and Linked Equations Algorithm Revised) Part I: Mathematical Formulation and Solution Procedure , Numer. Heat Transfer B , vol. 45 , pp. 1 – 17 , 2004 .
   Web of Science ®Google Scholar
• Z. G. Qu , Study on Advanced Numerical Algorithms on Fluid Flow and Heat Transfer Problems and Their Applications in Air Convective Heat Transfer Enhancement, Ph.D. thesis, Xi'an Jiaotong University, Xi'an, Shaanxi, PRC, 2005 (in Chinese) .
   Google Scholar
• J. Z. Zhang , Z. G. Qu , Y. L. He , and W. Q. Tao , Convergence, and Robustness Characteristics Comparison between CLEAR Algorithm, and SIMPLE Series Algorithms , J. Eng. Thermophys. , vol. 29 , pp. 2111 – 2114 , 2008 . (in Chinese) .
   Google Scholar
• Z. G. Wu , Z. G. Qu , Y.-L. He , and W. Q. Tao , A Comprehensive Performance Comparison for Segregated Algorithms of Flow and Heat Transfer in Complicated Geometries , Prog. Comput. Fluid Dynam. , vol. 8 , pp. 233 – 247 , 2008 .
   Web of Science ®Google Scholar
• P. K. Sweby , High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , SIAM J. Numer. Anal. , vol. 21 , pp. 995 – 1011 , 1984 .
   Web of Science ®Google Scholar
• P. L. Roe , Characteristic-Based Schemes for the Euler Equations , Annu. Rev. Fluid Mech. , vol. 18 , pp. 337 – 365 , 1986 .
   Web of Science ®Google Scholar
• B. Van Leer , Towards the Ultimate Conservative Difference Scheme. II. Monotoinity and Conservation Combined in a Second-Order Scheme , J. Comput. Phys. , vol. 14 , pp. 361 – 370 , 1974 .
   Web of Science ®Google Scholar
• P. H. Gaskell and A. K. C. Lau , Curvature-Compensated Convective Transport: SMART, a New Boundedness-Perserving Transport Algorithm , Int. J. Numer. Meth. Fluids , vol. 8 , pp. 617 – 641 , 1988 .
   Web of Science ®Google Scholar
• J. Zhu , A Low-Diffusive and Oscillation-Free Convective Scheme , Commun. Appl. Numer. Meth. , vol. 7 , pp. 225 – 232 , 1991 .
   Web of Science ®Google Scholar
• M. S. Darwish , A New High-Resolution Scheme Based on the Normalized Variable Formulation , Numer. Heat Transfer B , vol. 24 , pp. 353 – 371 , 1993 .
   Web of Science ®Google Scholar
• W. Gao , H. Li , Y. Liu , and Y. J. Jian , An Oscillation-Free High Order TVD/CBC-Based Upwind Scheme for Convection Discretization , Numer. Algor. , vol. 59 , pp. 29 – 50 , 2012 .
   Web of Science ®Google Scholar
• M. K. Kaibara , V. G. Ferreira , H. A. Navarro , J. A. Cuminato , A. Castelo , and M. F. Tomé , Upwind Schemes for Convection Dominated Problems, Proceedings of the 18th International Congress of Mechanical Engineering, Ouro Preto, MG, Brazil, 2005 .
   Google Scholar
• V. G. Ferreira , F. A. Kurokawa , A. B. Queiroz , M. K. Kaibara , C. M. Oishi , J. A. Cuminato , A. Castelo , M. F. Tomé and S. McKee , Assessment of a High-Order Finite Difference Upwind Scheme for the Simulation of Convection–Diffusion problems , Int. J. Numer. Meth. Fluids , vol. 60 , pp. 1 – 26 , 2009 .
   Web of Science ®Google Scholar
• M. A. Alves , P. J. Oliveira , and F. T. Pinho , A Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection, Int. J. Numer. Meth. Fluids , vol. 41, pp. 47–75, 2003.
   Web of Science ®Google Scholar
• C. H. Lin and C. A. Lin , Simple High-Order Bounded Convection Scheme to Model Discontinuities , AIAA J. , vol. 35 , no. 3 , pp. 563 – 565 , 1997 .
   Google Scholar
• B. Yu , W. Q. Tao , D. S. Zhang , and Q. W. Wang , Discussion on Numerical Stability and Boundedness of Convective Discretized Scheme , Numer. Heat Transfer B , vol. 40 , pp. 343 – 365 , 2001 .
   Web of Science ®Google Scholar
• X. Zhou , The Improvement of the Convection Scheme in Fluid Flow Equations , J. Suzhou Univ. (Nat. Sci. Ed.) , vol. 20 , no. 1 , pp. 18 – 22 , 2004 (in Chinese) .
   Google Scholar
• W. Q. Tao , Advances in Computational Heat Transfer , Science Press , Beijing , 2000 (in Chinese) .
   Google Scholar
• J. J. Wei , B. Yu , and W. Q. Tao , A New High-Order-Accurate and Bounded Scheme for Incompressible Flow , Numer. Heat Transfer B , vol. 43 , pp. 19 – 41 , 2003 .
   Web of Science ®Google Scholar
• M. L. Mason , L. E. Putnam , and R. J. Re , The Effect of Throat Contouring in Two-Dimensional Converging-Diverging Nozzles at Static Conditions, NASA TP 1704, 1980 .
   Google Scholar
• F. Moukalled and M. Darwish , A High-Resolution Pressure-Based Algorithm for Fluid Flow at All Speeds , J Comput. Phys. , vol. 168 , pp. 101 – 133 , 2001 .
   Web of Science ®Google Scholar
• Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/unhb.
   Google Scholar